Subtract 4 from both sides: -2x < -4. Then divide by -2 (reverse the inequality): x > 2.

-2x + 5 > 1 => -2x > -4 => x < 2.

-3x + 1 ≤ 4 => -3x ≤ 3 => x ≥ -1.

-4x + 1 < 3 => -4x < 2 => x > -0.5.

-x + 4 < 2 => -x < -2 => x > 2.

-x + 5 < 2 => -x < -3 => x > 3.

-x + 5 ≤ 2 => -x ≤ -3 => x ≥ 3.

2(x - 1) ≥ 3 => x - 1 ≥ 1.5 => x ≥ 2.5.

2(x - 1) ≥ 3x + 4 => 2x - 2 ≥ 3x + 4 => -x ≥ 6 => x ≤ -6.

2(x - 1) ≥ 4 => x - 1 ≥ 2 => x ≥ 3.

2x + 1 ≤ 3x - 4 => 1 + 4 ≤ x => x ≥ 5.

2x + 3 < 5x - 1 => 4 < 3x => x > 4/3.

2x + 3 ≥ 7 => 2x ≥ 4 => x ≥ 2.

2x + 4 < 3x - 1 => 5 < x => x > 5.

2x + 4 ≤ 10 => 2x ≤ 6 => x ≤ 3.

2x + 4 ≥ 8 => 2x ≥ 4 => x ≥ 2.

2x + 5 ≤ 3x - 1 => 5 + 1 ≤ 3x - 2x => 6 ≤ x => x ≥ 6.

2x - 4 > 0 => 2x > 4 => x > 2.

Add 7 to both sides: 2x < 10. Then divide by 2: x < 5.

3x + 1 ≤ 10 => 3x ≤ 9 => x ≤ 3.

3x + 2 ≤ 11 => 3x ≤ 9 => x ≤ 3.

3x + 4 ≤ 10 => 3x ≤ 6 => x ≤ 2.

3x + 5 ≥ 2x + 8 => x ≥ 3.

Add 7 to both sides: 3x ≤ 9. Then divide by 3: x ≤ 3.

6 - 2x ≤ 0 => -2x ≤ -6 => x ≥ 3.

6 - 3x ≤ 0 => -3x ≤ -6 => x ≥ 2.

7 - 3x > 1 => -3x > -6 => x < 2.

8x + 1 ≤ 5 => 8x ≤ 4 => x ≤ 0.5.

x + 2 > 3 => x > 1.

Solving gives sin(x) = -√3/2, so x = 7π/6 and 11π/6.